Ultraheavy asymmetric dark matter (DM) particles captured by compact stars can thermalize, self-gravitate, and collapse to form an endoparasitic black hole (EBH), whose subsequent growth may transmute the host star into a black hole. The continued existence of old millisecond pulsars (MSPs) and white dwarfs (WDs) thus places powerful constraints on the DM particle mass $m_{\chi }$ and the DM-nucleon scattering cross section ${\sigma }_{\mathrm{n}\chi }$. In this work, we derive an analytical expression for the transmutation timescale by solving the EBH growth equation while consistently accounting for the Bondi accretion of stellar matter, Hawking evaporation, and allowing for the possibility of sustained DM feeding of the EBH in a steady-state capture regime. We also incorporate quantum mechanical effects in the baryonic accretion process by modeling particle absorption in regimes where the hydrodynamic description breaks down, thereby providing a unified treatment of EBH growth across both particle and fluid regimes. Adopting a physically transparent collapse criterion for both fermionic and bosonic asymmetric DM, we compute the EBH transmutation timescales for representative MSPs and WDs residing in environments with different DM densities. Although the underlying physical ingredients are broadly the same as those considered in previous studies, the present work derives updated constraints through a closed-form analytical treatment of EBH growth, together with the adopted prescription for the EBH formation timescale. Consequently, we obtain a lower critical EBH mass for sustained growth and revised transmutation timescales. Requiring the transmutation time to exceed $\sim 1\mathrm{Gyr}$ for MSPs and $\sim 10\mathrm{Gyr}$ for WDs, we derive revised constraints on ${\sigma }_{\mathrm{n}\chi }$ over the DM mass range ${10}^6–{10}^{14}\mathrm{GeV}$. Notably, we show that EBHs with initial masses as small as $\sim 4\times {10}^4\mathrm{kg}$ can undergo sustained growth, thereby extending the region of the DM parameter space that can be probed using compact stars.

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• Classical black holes
• Dark matter
• General relativity
• Accretion disk & black-hole plasma
• Astronomical black holes
• Neutron stars & pulsars
• Stars